L070 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.
Two similar solids have lengths ratio 3:4 and smaller surface area 54 cm². Find larger area.
Area ratio 9:16; 54×16/9=96 cm².
Volume ratio of similar solids is 27:64. Find length and area ratios.
Length ratio 3:4; area ratio 9:16.
Lesson L070: Area and volume scale factors
Objective: Connect linear scale factors with area and volume change at the appropriate tier.
60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.
I selected the correct geometric fact, theorem, formula or transformation and used a clear diagram with appropriate labels and units.
I will name the fact or theorem, show the substitution or construction step and check whether the size, direction and units of the result are reasonable.
Stretch: Two similar solids have lengths ratio 3:4 and smaller surface area 54 cm². Find larger area.
Deep challenge: Volume ratio of similar solids is 27:64. Find length and area ratios.